Angle and Triangle Relationships

Standard

Degrees

A degree is a unit of measurement used to measure angles.

We can measure all Angles in Degrees.

There are 360 degrees in one Full Rotation (one
complete circle around

The Degree Symbol: °

We use a little circle ° following the number to mean degrees.

For example 90° means 90 degrees

Angles

types of angle

In One Diagram

This diagram might make it easier to remember:

Also: Acute, Obtuse and Reflex are in alphabetical order.

Supplementary Angles

Two Angles are Supplementary if they add up to 180 degrees.
These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°.

Notice that together they make astraight angle.

But the angles don’t have to be together.

These two are supplementary because 60° + 120° = 180°

Complementary Angles

Two angles are Complementary when they
add up to 90 degrees
(a Right Angle right angle).

These two angles (40° and 50°) are
Complementary Angles, because they add up to 90°.Notice that together they make a right angle right angle.
But the angles don’t have to be together.

These two are complementary because 27° + 63° = 90°

Angle Relationships

Interior Angle

An Interior Angle is an angle inside a shape.

Exterior Angle

The Exterior Angle is the angle between any side of a shape, and a line extended from the next side.

Angles On One Side of A Straight Line

Angles on one side of a straight line will always add to 180 degrees.

If a line is split into 2 and you know one angle you can always find the other one.


30° + 150° = 180°

Interior Angles of Polygons

An Interior Angle is an angle inside a shape.

Triangles

The Interior Angles of a Triangle add up to 180°

90° + 60° + 30° = 180°

80° + 70° + 30° = 180°

It works for this triangle!

Let’s tilt a line by 10° …

It still works, because one angle went up by 10°, but the other went down by 10°

Quadrilaterals (Squares, etc)

(A Quadrilateral has 4 straight sides)

90° + 90° + 90° + 90° = 360°

80° + 100° + 90° + 90° = 360°

A Square adds up to 360°

Let’s tilt a line by 10° … still adds up to 360°!

The Interior Angles of a Quadrilateral add up to 360°

Because there are Two Triangles in a Square

The interior angles in this triangle add up to 180°

(90°+45°+45°=180°)

… and for this square they add up to 360°

… because the square can be made from two triangles!

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s